v2.80: Keyboard Shortcut for Import / Export STL Files
You can do this off course (this is Blender)

The fastest way is to mouse right click on export stl button and assign a short cut. (you can press nothing but click other area to left it be empty keymap)



After you assign a shortcut to it, go into setting panel and the keymap setting, the setting of export/import will be included in Windows group:



You can assign different key map for it, and also all option that you can find on the exporting panel. The options will appear grey-out, which indicate that it is using default parameters. You can click on any of them to change the setting, override it. In your case, check the selection only button.